"As soon as we reach a level that will be comfortable for us and when it answers our interests and when we agree on acceptable conditions, then we will talk about signing (the deal)," Yanukovych was quoted as saying.
At the same, Yanukovych indicated he would attend a summit in Vilnius, Lithuania that opens on Thursday for further negotiations.
The announcement came as Russian President Vladimir Putin quashed claims by top Ukrainian officials that Moscow has offered Kiev discounts for Russian natural gas in return for Kiev's refusal to sign the EU deal.
Putin also urged the EU to engage in trilateral talks with Kiev in Moscow to settle all disputes.
Meanwhile, the round-the-clock protests continued in Kiev. Several thousand protesters, including university students who ditched lectures, rallied on two central squares Tuesday night. The demonstrators were joined by Loreta Grauziniene, the speaker of the Lithuanian parliament, who said that Ukraine's future belongs with Europe.
"Lithuania believes in the right choice of the Ukrainian people," Grauziniene told the crowd. "Lithuania and Ukraine will be in a united Europe together."
"We feel ourselves to be part of Europe and now the authorities want to take this identity away from us," said Yehor Mnishek, a student from Kiev. "It's like cutting off someone's arm or head."
As Kiev intensified talks with Brussels in recent months, Russia restricted imports of Ukrainian steel, chocolates and other products, which Ukrainian Prime Minister Mykola Azarov said reduced this year's exports by $6.5 billion. Still, Azarov described Ukrainian-Russian relations as "absolutely normal," and instead blamed Kiev's turnaround on Brussels, saying it refused to provide financial aid to the struggling Ukrainian economy.
"Let us say this straight away: The European Union provided no help for us here, other than general declarations," Azarov told foreign reporters. "We received no concrete help."
EU officials have countered that the deal brings enough economic benefits, such as foreign investment and greater access to European markets to outweigh the negative consequences.
Ukraine's decision was seen as a big victory for Russia, which does not want to lose its big Slavic neighbor which had long been part of the Russian and Soviet empires to the West. In a sign of rapprochement, Russia announced on Tuesday that it would lift its ban on Ukrainian chocolates, which it deemed unsafe just a few months ago.
More rallies were planned in the run-up to the summit and over the weekend. While the protests have been largely peaceful, there have been several scuffles between radical activists and riot police in which tear gas was used. Azarov said that police will treat protesters with respect, but will not allow provocations.
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Associated Press writer Raf Casert contributed to this story from Brussels.